Find Zeros of Polynomial Function

Discussion in 'Other Pre-University Math' started by nycmathguy, Sep 20, 2021.

  1. nycmathguy

    nycmathguy

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    Section 2.5
    Question 56


    20210919_211300.jpg

    Can you do 56 as a guide for me to do the rest on my own?
     
    nycmathguy, Sep 20, 2021
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  2. nycmathguy

    MathLover1

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    56.

    f(x)=2x^3+3x^2+18x+27

    given zero: 3i -> so we will also have -3i

    factors are (x-3i) and (x+3i)

    their product is: (x-3i) (x+3i)=x^2-(3i)^2=x^2-9(-1)=x^2+9

    use long division
    ..........(2x+3
    x^2+9| 2x^3+3x^2+18x+27
    ..........2x^3+0*x^2+18x
    ......................3x^2+27
    .........................3x^2+27
    ...................................0

    last factor is 2x+3 and third zero is
    2x+3=0
    2x=-3
    x=-3/2

    so, zeros are: 3i, -3i, -3/2
     
    MathLover1, Sep 21, 2021
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  3. nycmathguy

    nycmathguy

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    In terms of long division, what term is the dividend and which one is the divisor?
     
    nycmathguy, Sep 21, 2021
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  4. nycmathguy

    MathLover1

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    The number that is being divided (in this case, 2x^3+3x^2+18x+27) is called the dividend,
    and the number that it is being divided by (in this case, x^2+9) is called the divisor.
     
    MathLover1, Sep 22, 2021
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  5. nycmathguy

    nycmathguy

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    I could not make out the difference between the dividend and divisor as typed in your first reply.
     
    nycmathguy, Sep 22, 2021
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  6. nycmathguy

    MathLover1

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    I write it similar to this
    upload_2021-9-21_19-34-47.jpeg

    I do it this way

    .............(
    x^2+9 | 2x^3+3x^2+18x+27
     
    MathLover1, Sep 22, 2021
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  7. nycmathguy

    nycmathguy

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    I now see what you're talking about. Cool. Taking a little break from math for the rest of this week. Need to rest my brain cells.
     
    nycmathguy, Sep 22, 2021
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  8. nycmathguy

    MathLover1

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    ok
     
    MathLover1, Sep 22, 2021
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  9. nycmathguy

    nycmathguy

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    I enjoy solving math problems but I need a short break. Be back Friday, Lord willing, with more questions from Section 2.6.
     
    nycmathguy, Sep 22, 2021
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